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Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…

Computation · Statistics 2026-05-19 Anderson V. Pires , Maliki Moustapha , Stefano Marelli , Bruno Sudret

We present batching as an omnibus device for uncertainty quantification using simulation output. We consider the classical context of a simulationist performing uncertainty quantification on an estimator $\theta_n$ (of an unknown fixed…

Methodology · Statistics 2024-08-27 Yongseok Jeon , Yi Chu , Raghu Pasupathy , Sara Shashaani

In stochastic simulation, input uncertainty refers to the propagation of the statistical noise in calibrating input models to impact output accuracy, in addition to the Monte Carlo simulation noise. The vast majority of the input…

Methodology · Statistics 2024-03-18 Motong Chen , Henry Lam , Zhenyuan Liu

In construction projects, contingency reserves have traditionally been estimated based on a percentage of the total project cost, which is arbitrary and, thus, unreliable in practical cases. Monte Carlo simulation provides a more reliable…

Applications · Statistics 2024-06-07 David Curto , Fernando Acebes , Jose M Gonzalez-Varona , David Poza

In this paper, we present a unified framework for decision making under uncertainty. Our framework is based on the composite of two risk measures, where the inner risk measure accounts for the risk of decision given the exact distribution…

Optimization and Control · Mathematics 2015-01-07 Pengyu Qian , Zizhuo Wang , Zaiwen Wen

ML models have errors when used for predictions. The errors are unknown but can be quantified by model uncertainty. When multiple ML models are trained using the same training points, their model uncertainties may be statistically…

Machine Learning · Statistics 2025-09-23 Xiaoping Du

In the context of Monte Carlo (MC) simulation of particle transport Uncertainty Quantification (UQ) addresses the issue of predicting non statistical errors affecting the physical results, i.e. errors deriving mainly from uncertainties in…

Computational Physics · Physics 2015-06-18 Paolo Saracco , Maria Grazia Pia

Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty…

Machine Learning · Statistics 2025-12-01 Eliot Wong-Toi , Alex Boyd , Vincent Fortuin , Stephan Mandt

In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…

Methodology · Statistics 2023-10-27 Kimia Vahdat , Sara Shashaani

We consider a simulation-based Ranking and Selection (R&S) problem with input uncertainty, where unknown input distributions can be estimated using input data arriving in batches of varying sizes over time. Each time a batch arrives,…

Optimization and Control · Mathematics 2022-09-05 Di Wu , Yuhao Wang , Enlu Zhou

Systemic risk measures were introduced to capture the global risk and the corresponding contagion effects that is generated by an interconnected system of financial institutions. To this purpose, two approaches were suggested. In the first…

Optimization and Control · Mathematics 2024-02-23 Sarah Kaakai , Anis Matoussi , Achraf Tamtalini

Risk management is particularly concerned with extreme events, but analysing these events is often hindered by the scarcity of data, especially in a multivariate context. This data scarcity complicates risk management efforts. Various tools…

Methodology · Statistics 2026-01-15 Nisrine Madhar , Juliette Legrand , Maud Thomas

Uncertainty quantification is crucial for building reliable and trustable machine learning systems. We propose to estimate uncertainty in recurrent neural networks (RNNs) via stochastic discrete state transitions over recurrent timesteps.…

Machine Learning · Computer Science 2020-11-25 Cheng Wang , Carolin Lawrence , Mathias Niepert

In this article, we address the problem of risk assessment of stealthy attacks on uncertain control systems. Considering data injection attacks that aim at maximizing impact while remaining undetected, we use the recently proposed…

Optimization and Control · Mathematics 2023-09-26 Sribalaji C. Anand , André M. H. Teixeira , Anders Ahlén

In this paper, we present an approach for quantifying the propagated uncertainty of robot systems in an online and data-driven manner. Especially in Human-Robot Collaboration, keeping track of the safety compliance during run time is…

Robotics · Computer Science 2023-02-22 Woo-Jeong Baek , Torsten Kröger

Machine learning models are often evaluated using point estimates of performance metrics such as accuracy, F1 score, or mean squared error. Such summaries fail to capture the inherent variability induced by stochastic elements of the…

Machine Learning · Computer Science 2026-05-13 Christoph Lehmann , Yahor Paromau

Measuring and managing risk has become crucial in modern decision making under stochastic uncertainty. In two-stage stochastic programming, mean risk models are essentially defined by a parametric recourse problem and a quantification of…

Optimization and Control · Mathematics 2016-11-28 Matthias Claus , Volker Krätschmer , Rüdiger Schultz

Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…

Machine Learning · Computer Science 2024-04-22 Paul Hofman , Yusuf Sale , Eyke Hüllermeier

This paper firstly addresses the problem of risk assessment under false data injection attacks on uncertain control systems. We consider an adversary with complete system knowledge, injecting stealthy false data into an uncertain control…

Systems and Control · Electrical Eng. & Systems 2022-12-12 Sribalaji C. Anand , André M. H. Teixeira , Anders Ahlén

We address the problem of uncertainty quantification and propose measures of total, aleatoric, and epistemic uncertainty based on a known decomposition of (strictly) proper scoring rules, a specific type of loss function, into a divergence…

Machine Learning · Computer Science 2025-05-29 Paul Hofman , Yusuf Sale , Eyke Hüllermeier